She said the couple struggled for months trying to choose a name and made a decision to wait until the baby was born to figure out which one fitted best.

She said Neve meant bright, radiant and snow.

New Zealand Prime Minister Jacinda Ardern announced on Sunday she had named her new-born daughter Neve Te Aroha as she prepared to leave hospital amidst an outpouring of public excitement.

She and Mr Gayford had opted to spell the name Neve - as opposed to Niamh, for example - for simplicity, with Ms Ardern joking about the unusual spellings of Clarke and Jacinda.

Aroha means "love" in Maori, while Mt Te Aroha is a 952-metre mountain in the Kaimai Range, on New Zealand's North Island.

"All of the names that were gifted along the way, I thought how do I reflect the generosity, particularly from all the iwi (Maori tribes) who gifted us names and Te Aroha seemed to me to be a way we could show that love and generosity", Ardern explained.

Ardern is only the second world leader to give birth while in office, after former Pakistan PM Benazir Bhutto, and said she hoped such experiences would not be unusual in the future.

Ms Ardern said "the moment happened so quickly".

At almost three days old the tiny tot will make her first public appearance at 11am cradled in mother Jacinda Ardern's arms with proud dad Clarke Gayford.

"We really just wanted to say thank you and that we're all doing really well".

He plans to become the primary caregiver for the child when Ardern returns to work following a leave of six weeks.

Ardern has had little sleep over the past few days, with the baby also described as being "very alert and one hungry baby".

Ardern said she "feels very lucky" and thanked everyone for their best wishes after the birth, as she updated her social media accounts from the comfort of her hospital bed. Arden will take six weeks of leave with Deputy Prime Minister Winston Peters assuming the role of Acting Prime Minister.

"Those moments have mattered as much to us as any of those lovely messages of support from around the world", she said.

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